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Simplifying 145.6 = x(x + 0.12) Reorder the terms: 145.6 = x(0.12 + x) 145.6 = (0.12 * x + x * x) 145.6 = (0.12x + x2) Solving 145.6 = 0.12x + x2 Solving for variable 'x'. Reorder the terms: 145.6 + -0.12x + -1x2 = 0.12x + -0.12x + x2 + -1x2 Combine like terms: 0.12x + -0.12x = 0.00 145.6 + -0.12x + -1x2 = 0.00 + x2 + -1x2 145.6 + -0.12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 145.6 + -0.12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -145.6 + 0.12x + x2 = 0 Move the constant term to the right: Add '145.6' to each side of the equation. -145.6 + 0.12x + 145.6 + x2 = 0 + 145.6 Reorder the terms: -145.6 + 145.6 + 0.12x + x2 = 0 + 145.6 Combine like terms: -145.6 + 145.6 = 0.0 0.0 + 0.12x + x2 = 0 + 145.6 0.12x + x2 = 0 + 145.6 Combine like terms: 0 + 145.6 = 145.6 0.12x + x2 = 145.6 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 145.6 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 145.6 + 0.0036 Combine like terms: 145.6 + 0.0036 = 145.6036 0.0036 + 0.12x + x2 = 145.6036 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 145.6036 Calculate the square root of the right side: 12.066631676 Break this problem into two subproblems by setting (x + 0.06) equal to 12.066631676 and -12.066631676.Subproblem 1
x + 0.06 = 12.066631676 Simplifying x + 0.06 = 12.066631676 Reorder the terms: 0.06 + x = 12.066631676 Solving 0.06 + x = 12.066631676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 12.066631676 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 12.066631676 + -0.06 x = 12.066631676 + -0.06 Combine like terms: 12.066631676 + -0.06 = 12.006631676 x = 12.006631676 Simplifying x = 12.006631676Subproblem 2
x + 0.06 = -12.066631676 Simplifying x + 0.06 = -12.066631676 Reorder the terms: 0.06 + x = -12.066631676 Solving 0.06 + x = -12.066631676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -12.066631676 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -12.066631676 + -0.06 x = -12.066631676 + -0.06 Combine like terms: -12.066631676 + -0.06 = -12.126631676 x = -12.126631676 Simplifying x = -12.126631676Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.006631676, -12.126631676}
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